The present disclosure relates to a method for determining a switching function for a sliding mode controller for controlling a controlled variable of a system and to a sliding mode controller and to a use of such a controller.
Controlling hydraulic valves, for example hydraulic directional valves, is a demanding task on account of technical and non-technical requirements. In such valves, a volumetric flow of a hydraulic fluid is controlled using the position of a piston which moves inside the valve body. In this case, the position of the piston itself is controlled, for example, by means of an electromagnet or two counteracting electromagnets.
In this case, the magnet(s) is/are accordingly counteracted by one or two control springs which center the piston at a hydraulic zero point if the magnets are not energized. Furthermore, static friction and sliding friction also act inside the valves and need to be taken into account when controlling the valves, just like magnetic hysteresis and eddy current effects inside the corresponding magnetic circuits. In addition, flow forces occur on the slider or the piston when there is a flow through the valve, which likewise has to be taken into account during control.
These properties of hydraulic valves impose high demands on a position controller of the piston. A combination of a PI controller with state feedback, for example, can be used to control the piston position of hydraulic directional valves. Such a controller is then usually supplemented with non-linearities in the P and I branches in order to adapt the gains of the individual branches independently of one another for different signal ranges and to take into account the properties of the controlled system, that is to say the valve. However, these non-linearities result in a large number of coupled parameters which are typically manually interpreted when designing a controller.
For this purpose, step responses of different step heights are then usually measured and the controller parameters are varied until the system behavior corresponds to the desired requirements. One approach for automating such a procedure is known, for example, from Krettek et al: “Evolutionary hardware-in-the-loop optimization of a controller for cascaded hydraulic valves”, IEEE/ASME International Conference on Advanced Intelligent Mechatronics, 1-6, 2007.
However, development and activation times of such controllers and the associated costs are subject to ever more restrictive budgeting, with the result that a conventional design of controllers for hydraulic valves is becoming more and more difficult.
It is therefore desirable to provide a controller, for example for hydraulic valves, which, on the one hand, is simple to parameterize and, on the other hand, provides the same control quality as previously used controllers with a reduced complexity.